No doubt .... if the choice is between March and April definately go in April. Not only is the weather in most years better at that time, there are a number of factors beyond rainfall amounts to consider. I am not sure where you got the impression that there is less rain in March, nor if that is actually the case. Know that earlier in the year you are more likely to encounter snowstorms over the mountains. It can make the going more difficult. Of course in any given year is remains possible, although less likely, for April weather to be worse than in March.
Snow melt trickling down the mountains creates mud along the Camino. Not just surface mud, but in some places it is well deeper than ankle level. The mud can be clay like, sticking to your boots/shoes making walking difficult. Trekking through the mud was for me a far bigger challenge than any rains. And not a challenge in a pleasant sort of way. Such conditions are usually far worse in March than in April.
Europe, and Spain in particular, seems to go into hibernation during the winter months. March is still winter. Spring only seems to arrive in April. Some of the albergues are closed until April. Many outdoor sections of cafes and restaurants are empty during March if the establishments are even yet open at all for the season. At the end of a day when looking for something to do the options are more limited in March. It can feel like you are in a ghost town as things have not yet come alive for the year.
The hours of daylight are longer in April.
I walked in March 2010, a busy Holy Year. The weather overall was mixed. There were perfect days, and then there were times of heavy cold rain accompanied by gale force winds. There were snow storms that made walking difficult. In fact going through the pass after O'Cebreiro the Civil Guard was plucking pilgrims off the mountain because of the dangerous conditions. It was not fun.
Although I like solitude at times, there were a few days when I did not see another pilgrim walking the entire day. Thus the option of walking with other people wasn't always possible. Had I twisted an ankle or otherwise had an injury of some sort, I might have frozen to death waiting for assistance. This was on my mind and was a little unnerving in certain places. April has a higher number of pilgrims along the entire Camino yet is not overly crowded. That is unless you are between Sarria and Santiago during the week leading up to and the week following Easter. (Easter falls on 31 March in 2013).
March was colder than I antipated it would be. While I had been expecting Spring-like weather, It was still very much winter. Foolishly in terms of clothing I hadn't been prepared for the cold.
March, April ... both are good. Based on my experience, for reasons described above again I recommend April.
Buen Camino whichever you decide!